Problem: Find $A$ and $B$ such that
\[\frac{5x+2}{x^2-7x-30}=\frac{A}{x-10}+\frac{B}{x+3}.\]Write your answer in the form $(A,B)$.
Explanation: We factor the denominator in the left-hand side to get \[\frac{5x+2}{(x-10)(x+3)}= \frac{A}{x - 10} + \frac{B}{x + 3}.\]We then multiply both sides by $(x - 10)(x + 3)$, to get \[5x + 2 = A(x + 3) + B(x - 10).\]We can solve for $A$ and $B$ by substituting suitable values of $x$.  For example, setting $x = 10$, the equation becomes $52 = 13A$, so $A = 4$.  Setting $x = -3$, the equation becomes $-13 = -13B$, so $B = 1$.  Therefore, $(A,B) = \boxed{(4,1)}$.